Problem: Solve for $k$, $ -\dfrac{8}{5k} = -\dfrac{5k + 10}{5k} - \dfrac{5}{4k} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5k$ $5k$ and $4k$ The common denominator is $20k$ To get $20k$ in the denominator of the first term, multiply it by $\frac{4}{4}$ $ -\dfrac{8}{5k} \times \dfrac{4}{4} = -\dfrac{32}{20k} $ To get $20k$ in the denominator of the second term, multiply it by $\frac{4}{4}$ $ -\dfrac{5k + 10}{5k} \times \dfrac{4}{4} = -\dfrac{20k + 40}{20k} $ To get $20k$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{5}{4k} \times \dfrac{5}{5} = -\dfrac{25}{20k} $ This give us: $ -\dfrac{32}{20k} = -\dfrac{20k + 40}{20k} - \dfrac{25}{20k} $ If we multiply both sides of the equation by $20k$ , we get: $ -32 = -20k - 40 - 25$ $ -32 = -20k - 65$ $ 33 = -20k $ $ k = -\dfrac{33}{20}$